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Physical review. B./Physical review. B

Interplay of alternation and further neighbor interaction in S=12 spin chains: A case study of Cs2CuAl4O8

Badiur Rahaman, Satyaki Kar, Alexander N. Vasiliev, Tanusri Saha‐Dasgupta

Published Oct 8, 2018• 9 citations
Publisher

Abstract

Using Wannier function formulation and total energy calculations by first-principles density functional theory (DFT), we derive the underlying spin model of a recently synthesized compound, ${\mathrm{Cs}}_{2}{\mathrm{CuAl}}_{4}{\mathrm{O}}_{8}$, having zeolitelike network structure. The computed magnetic interactions show that the interchain Cu-Cu interactions are negligibly small compared to intrachain Cu-Cu interactions, thus characterizing ${\mathrm{Cs}}_{2}{\mathrm{CuAl}}_{4}{\mathrm{O}}_{8}$ as a prototypical one-dimensional (1D) spin-$\frac{1}{2}$ system. Interestingly, the DFT-derived 1D spin model features a combination of alternating ferromagnetic-antiferromagnetic interactions, together with the presence of both nearest- and next-nearest-neighbor interactions, making it an unprecedented case. The solution of the derived spin model of the compound using the quantum Monte Carlo technique shows reasonably good agreement with the experimental susceptibility data, measured in the presence of the magnetic field. The presence of spin gap is suggested by quantum Monte Carlo simulations in the zero-field condition, which is cross-checked by a more rigorous exact diagonalization study. Motivated by the intricacy of the derived spin model, we further examine the ground-state properties of this model in the parameter space of exchange interactions, which shows the possibility of driving quantum phase transition between gapped and gapless spin excitation. Our study is expected to shed light on the fascinating world of 1D quantum spin systems.

DOI
10.1103/physrevb.98.144412

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Using Wannier function formulation and total energy calculations by first-principles density functional theory (DFT), we derive the underlying spin model of a recently synthesized compound, Cs2CuAl4O8{\mathrm{Cs}}_{2}{\mathrm{CuAl}}_{4}{\mathrm{O}}_{8}Cs2​CuAl4​O8​, having zeolitelike network structure. The computed magnetic interactions show that the interchain Cu-Cu interactions are negligibly small compared to intrachain Cu-Cu interactions, thus characterizing Cs2CuAl4O8{\mathrm{Cs}}_{2}{\mathrm{CuAl}}_{4}{\mathrm{O}}_{8}Cs2​CuAl4​O8​ as a prototypical one-dimensional (1D) spin-12\frac{1}{2}21​ system. Interestingly, the DFT-derived 1D spin model features a combination of alternating ferromagnetic-antiferromagnetic interactions, together with the presence of both nearest- and next-nearest-neighbor interactions, making it an unprecedented case. The solution of the derived spin model of the compound using the quantum Monte Carlo technique shows reasonably good agreement with the experimental susceptibility data, measured in the presence of the magnetic field. The presence of spin gap is suggested by quantum Monte Carlo simulations in the zero-field condition, which is cross-checked by a more rigorous exact diagonalization study. Motivated by the intricacy of the derived spin model, we further examine the ground-state properties of this model in the parameter space of exchange interactions, which shows the possibility of driving quantum phase transition between gapped and gapless spin excitation. Our study is expected to shed light on the fascinating world of 1D quantum spin systems.
Magnon excitations in Cs2CuAl4O8Cs_2CuAl_4O_8Cs2​CuAl4​O8​ - a bond alternating S=1/2 spin chain with next nearest neighbor coupling
A recent density functional theory (DFT) based analysis, complemented with Quantum Monte Carlo calculations revealed a highly spin-frustrating nature of the one-dimensional spin-12\frac{1}{2}21​ compound Cs2CuAl4O8Cs_2CuAl_4O_8Cs2​CuAl4​O8​ that comprises of unique bond alternations and relatively strong next nearest neighbor interactions. This article gives a brief account on possible magnon excitations that can appear in the ground state of such systems. We find that the spin waves obtained on top of coplanar helical reference states show multiple magnon modes (both acoustic and optical). However, those magnon modes turn out to be stable only in the absence of bond alternations.
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We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J1FJ_1^FJ1F​) and antiferromagnetic (J1AJ_1^AJ1A​) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (J2FJ_2^FJ2F​). In this model frustration is induced by the non-zero J2FJ_2^FJ2F​ and the effect of dimerization is realized by changing the strength of J1AJ_1^AJ1A​ for a fixed value of J1FJ_1^FJ1F​. The model with site spin sss behaves like a Haldane spin chain with site spin 2sss in the limit of vanishing J2FJ_2^FJ2F​ and large J1F/J1AJ_1^F/J_1^AJ1F​/J1A​. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of J1A−J2FJ_1^A-J_2^FJ1A​−J2F​ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
The spin-1/21/21/2 Heisenberg chain with a ferromagnetic first-neighbor exchange coupling J1{J}_{1}J1​ and an antiferromagnetic second-neighbor J2{J}_{2}J2​ has a Haldane dimer ground state with an extremely small spin gap. Thus the ground state is readily altered by perturbations. Here, we investigate the effects of XXZ exchange magnetic anisotropy of both the easy-axis and easy-plane types and an alternation in J1{J}_{1}J1​ on the ground state, the spin gap, and magnetic properties of the frustrated ferromagnetic spin-1/21/21/2 chain. It is found that there are two distinct dimerized spin-gap phases, in one of which the spin gap and the magnetic susceptibility are extremely small around the SU(2) symmetric case and in the other they are moderately large far away from the SU(2) symmetric case. A small alternation in the amplitude of J1{J}_{1}J1​ rapidly shortens the pitch of spin correlations towards the four-spin periodicity, as in the limit of ${J}_{1}/{J}_{2}\ensuremath{\rightarrow}0$. These effects are not sufficient to quantitatively explain overall experimentally observed magnetic properties in the quasi-one-dimensional spin-gapped magnetoelectric cuprate Rb2Cu2Mo3O12{\mathrm{Rb}}_{2}{\mathrm{Cu}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}Rb2​Cu2​Mo3​O12​ that exhibits ferroelectricity stabilized by a magnetic field. Our results are also relevant to Cs2Cu2Mo3O12{\mathrm{Cs}}_{2}{\mathrm{Cu}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}Cs2​Cu2​Mo3​O12​, where the ferromagnetic intrachain and antiferromagnetic interchain order has recently been found, in a single chain level. We also reveal the nature of symmetry-protected topological phase transitions in the model by mapping onto effective spin-1 chain models.
A one-dimensional spin-1∕2 model in which the alternation of the exchange interactions between neighboring spins is accompanied by the next-nearest-neighbor (NNN) spin exchange (zig-zag spin ladder with alternation) is studied. The thermodynamic characteristics of the model quantum spin chain are obtained in the mean-field-like approximation. Depending on the strength of the NNN interactions, the model manifests either the spin-gapped behavior of low-lying excitations at low magnetic fields, or ferrimagnetic ordering in the ground state with gapless low-lying excitations. The system undergoes second-order or first-order quantum phase transitions, governed by the external magnetic field, NNN coupling strength, and the degree of the alternation. Hence, NNN spin–spin interactions in a dimerized quantum spin chain can produce a spontaneous magnetization. On the other hand, for quantum spin chains with a spontaneous magnetization, caused by NNN spin–spin couplings, the alternation of nearest-neighbor (NN) exchange interactions can cause destruction of that magnetization and the onset of a spin gap for low-lying excitations. Alternating NN interactions produce a spin gap between two branches of low-energy excitations, and the NNN interactions yield asymmetry of the dispersion laws of those excitations, with possible minima corresponding to incommensurate structures in the spin chain.
A frustrated spin-1/21/21/2 XXZ chain model comprising a ferromagnetic nearest-neighbor coupling with the bond alternation, ${J}_{1}(1\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta})<0$, and an antiferromagnetic second-neighbor exchange coupling J2>0{J}_{2}>0J2​>0 is studied at zero and weak magnetic fields by means of density-matrix renormalization-group calculations of order parameters, correlation functions, and the entanglement entropy, as well as an Abelian bosonization analysis. At zero magnetic field, the bond alternation $\ensuremath{\delta}>0$ suppresses the gapless phase characterized by a vector-chiral (VC) long-range order (LRO) and a quasi-LRO of an incommensurate spin spiral, whereas this phase occupies a large region in the space of J1/J2{J}_{1}/{J}_{2}J1​/J2​ and the easy-plane exchange anisotropy for $\ensuremath{\delta}=0$ [S. Furukawa et al., Phys. Rev. Lett. 105, 257205 (2010)]. Then, four gapped phases are found to appear as the exchange anisotropy varies from the SU(2)-symmetric case to the U(1)-symmetric case: the Haldane dimer (D+{}_{+}+​) phase with the same sign of the x,yx,yx,y- and zzz-component dimer order parameters, two VC dimer (VCD+{}_{+}+​/VCD${}_{\ensuremath{-}}$) phases with the sign of the zzz-component dimer order parameter being unaltered/reversed, and the even-parity dimer (D${}_{\ensuremath{-}}$) phase. At small magnetic fields, a field-induced ring-exchange interaction, which is proportional to a staggered scalar chirality and a magnetic flux penetrating the associated triangle, drives a transition from the D${}_{\ensuremath{-}}$ phase into a VC-Neel-dimer (VCND) phase, but not from the D+{}_{+}+​ phase. This VCND phase is stable up to the large magnetic field at which the Zeeman term closes the spin gap. A possible relevance to Rb2{}_{2}2​Cu2{}_{2}2​Mo3{}_{3}3​O12{}_{12}12​ is discussed.